Combinatorics of Train Tracks. (AM-125), Volume 125 (eBook)

R. C. Penner, John L. Harer (Autoren)

eBook Download: PDF

2016 | 1. Auflage
232 Seiten
Princeton University Press (Verlag)
978-1-4008-8245-8 (ISBN)

Infos

Measured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry, and dynamical systems. This book presents a self-contained and comprehensive treatment of the rich combinatorial structure of the space of measured geodesic laminations in a fixed surface. Families of measured geodesic laminations are described by specifying a train track in the surface, and the space of measured geodesic laminations is analyzed by studying properties of train tracks in the surface. The material is developed from first principles, the techniques employed are essentially combinatorial, and only a minimal background is required on the part of the reader. Specifically, familiarity with elementary differential topology and hyperbolic geometry is assumed. The first chapter treats the basic theory of train tracks as discovered by W. P. Thurston, including recurrence, transverse recurrence, and the explicit construction of a measured geodesic lamination from a measured train track. The subsequent chapters develop certain material from R. C. Penner's thesis, including a natural equivalence relation on measured train tracks and standard models for the equivalence classes (which are used to analyze the topology and geometry of the space of measured geodesic laminations), a duality between transverse and tangential structures on a train track, and the explicit computation of the action of the mapping class group on the space of measured geodesic laminations in the surface.

Produkt-Details

• Erscheint lt. Verlag: 2.3.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Graphentheorie
• Themenwelt: Technik ► Fahrzeugbau / Schiffbau
• Schlagworte: Ambient isotopy • analytic function • Axiom • Brouwer fixed-point theorem • Cantor set • Cardinality • Change of basis • coefficient • combinatorics • Compactification (mathematics) • conjugacy class • Connected component (graph theory) • Connectivity (graph theory) • coordinate system • cotangent space • Covering space • CW complex • deformation theory • Dehn twist • diffeomorphism • Differential topology • Disjoint sets • Disjoint union • Disk (mathematics) • Eigenvalues and Eigenvectors • Embedding • Equation • equivalence class • Equivalence class (music) • equivalence relation • Euclidean space • Euler characteristic • Explicit formula • Explicit formulae (L-function) • fiber bundle • foliation • Fuchsian group • Geodesic Curvature • Geometry • Harmonic function • Homeomorphism • Homotopy • Horocycle • Hyperbolic Geometry • hyperbolic motion • hyperbolic space • Incidence matrix • Inequality (mathematics) • Infimum and supremum • Injective function • intersection number • Intersection number (graph theory) • Intersection (set theory) • Interval (mathematics) • Invariance of domain • invariant measure • Jordan Curve Theorem • Kähler manifold • Lexicographical order • Linear map • Linear subspace • Mapping class group • Mathematical Induction • Monogon • Natural topology • Orientability • Pair of pants (mathematics) • Parallel curve • parametrization • Parity (mathematics) • projective space • Quadratic differential • scientific notation • Sign (mathematics) • Special case • spectral radius • Standard basis • subsequence • Subset • Summation • Support (mathematics) • Symplectic Geometry • Symplectomorphism • Tangent • Tangent Space • Tangent vector • Teichmüller space • Theorem • Topological space • Topology • Total order • Train track (mathematics) • Transitive relation • transpose • Transversality (mathematics) • Transverse measure • uniformization theorem • Unit tangent bundle • Unit vector • Vector field
• ISBN-10: 1-4008-8245-1 / 1400882451
• ISBN-13: 978-1-4008-8245-8 / 9781400882458